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# Percents from fraction models

## Video transcript

- [Instructor] So we're told the square below represents one whole, so this entire square is a whole. And then they ask us what
percent is represented by the shaded area, so why
don't you pause this video and see if you can figure that out. So let's see. The whole is divided into
one, two, three, four, five, six, seven, eight,
nine, 10 equal sections, of which one, two, three, four, five, six, seven are actually filled in. That's the shaded area,
so one way to think about it is 7/10 are shaded in, but how do we express this
fraction as a percent? They're asking for a percent. Well remember, percent, it
literally means per hundred. Cent, same root as the word 100. You see it cents or century,
and so can we write this as per 100 instead of per 10? Well, seven per 10 is the same
thing as 70 per 100, or 70%. And how did I go from 7/10 to 70 over 100? Well, I just multiply both the numerator and the denominator by 10. And once you do more and more percents, you'll get a hang of it. You'll say, "Oh, 7/10. "That's the same thing as
70 per 100, which is 70%." Let's do another example. Here, we're told 100% is shown on the following tape diagram, so just this amount
right over here is 100%, and then they ask us what
percent is represented by the entire tape diagram, so by this entire thing right over here. Pause this video and see
if you can answer that. Well, one way to think about 100%, 100% is equivalent to a whole,
and now we have three times as much as that for the
entire tape diagram, so you could view this as three wholes, or you could say that's 100%. We have another 100% right over here. And then we have another
100% right over here, so the whole tape diagram,
that would be 300%. Let's do another example. This is strangely fun. (laughs) Okay, and I'll see. It says the large rectangle
below represents one whole. All right, so that's this
whole thing is one whole. What percentage is represented
by the shaded area? So pause the video and see if
you can figure that out again. So let's just express
it as a fraction first, so we have a total of one,
two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 squares. So out of those 20
squares, we see that six of them are actually shaded in. So 6/20, could we write that as per 100? Well, let's see. To go from 20 to 100, I multiply by five, and so if I multiply
the numerator by five, I'll get the same value. Six times five is 30, so
six per 20 is the same thing as 30 per 100, which is
the same thing as 30%, which literally means
per 100, so this is 30%. Let's do one last example. Here we are told each large rectangle below represents one
whole, so this is a whole, and then this whole thing right
over here is another whole. What percentage is represented
by the shaded area? Again, pause the video. See if you can answer that. So this one, we've shaded
in a whole, so that is 100%, and then over here, we have shaded in one, two, three, 4/5 of the whole. So 4/5, if I wanted to express it as per 100, what would it be? Well, five time 20 is 100,
so four times 20 is 80, so 4/5, or 80/100, is filled out here. We could say 80 per 100, which
is the same thing as 80%, so this right over here is 80%. So what percent is represented
by the shaded area? Well, we have 100%, and then
we have 80%, so we have 180%. It's more than a whole. If you have a percentage
that is larger than 100%, you're talking about
something that is more than a whole, and then we see that. We have a whole right over here, and then we have 80% more than that.